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#set page(width: 16cm, margin: 0.5em, height: auto)
#let definition(content) = box(fill: luma(92%), width: 100%, inset: 0.5em, stroke: black)[#content]
#let pr = $nu$
#let time = $t$
== Notations
#definition[
We denote :
- Pressure : $pr in [0,1]$
- time : $t >=0$
- point : defined by position $x$ and $y$ (or $p = (x,y) in RR^2$)
- Raw inputs are denoted by a tuple $i[k] = (pr[k], t[k], x[k],y[k])$ with $k in NN$.
]
#definition[
An _input stream_ is a sequence of raw inputs $i = (pr, t,x,y)$
- with time $t[k]$ $arrow.tr arrow.tr$ strictly increasing
- starts with a #raw("Down") event
- contains #raw("Move") for $k >=1$
- ends either with a #raw("Move") or a #raw("Up") . If it is a #raw("Up") we say the input stream is _complete_
]
#definition[
We addition define
- $v_x, v_y, a_x, a_y$ as the velocity and acceleration.
With the vector shorthand $v = (v_x,v_y) in RR^2$ and $a = (a_x, a_y) in RR^2$
]
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